List of practice Questions

The 4th term of a G.P. is square of its second term, and the first term is – 3. Determine its 7th term.
Which term of the following sequences: 

(a) 2 ,\(2\sqrt{2}\) , 4 ,.... is 128 ?

 (b) \(\sqrt{3}\), 3, \(3\sqrt{3}\),... is 729 ? 

(c) \(\frac{1}{3},\frac{1}{9},\frac{1}{27}\) ,.... is \(\frac{1}{19683}\) ?

Find the 20th and n th terms of the G.P. \(\frac{5 }{ 2} ,\frac{ 5}{ 4} ,\frac{ 5 }{ 8} \),......
Given a G.P. with a = 729 and 7th term 64, determine S7.
For what values of x, the numbers \(\frac{-2}{7}\), x , \(\frac{-7}{2}\) are in G.P.?
Find the sum to indicated number of terms in each of the geometric progressions in Exercises 7 to 10: 0.15, 0.015, 0.0015, ... 20 terms.
Find the sum to indicated number of terms in each of the geometric progressions in \(\sqrt{7},\sqrt{21},3\sqrt{7},\) ... n terms.
Find the sum to indicated number of terms in each of the geometric progressions in 1, – a, \(a^2\), –\(a^3\), ... n terms (if a ≠ – 1).
Find the sum to indicated number of terms in each of the geometric progressions in\(x^3,x^5,x^7\), ... n terms (if x ≠ ± 1).
Evaluate \(\displaystyle\sum_{k=1}^{11}\) (2 + 3k).
The sum of first three terms of a G.P. is \(\frac{39}{10}\) and their product is 1. Find the common ratio and the terms.
How many terms of G.P. \(3,3^2,3^3\), … are needed to give the sum 120?
The sum of first three terms of a G.P. is 16 and the sum of the next three terms is 128. Determine the first term, the common ratio and the sum to n terms of the G.P.
Find a G.P. for which sum of the first two terms is – 4 and the fifth term is 4 times the third term.
If the 4\(^{th}\), 10\(^{th}\) and 16\(^{th}\) terms of a G.P. are x, y and z, respectively. Prove that x, y, z are in G.P.
Find the sum of the products of the corresponding terms of the sequences 2, 4, 8,16, 32 and 128, 32, 8, 2, \(\frac{1}{2}\).

Show that the products of the corresponding terms of the sequences a, ar, ar2,…arn – 1 and A, AR, AR2, … ARn – 1 form a G.P, and find the common ratio.

Find four numbers forming a geometric progression in which the third term is greater than the first term by 9, and the second term is greater than the 4th by 18.
If the pth, qth and rth terms of a G.P. are a, b and c, respectively. Prove that \(a^{q-r} b^{r-p} c^{p-q}=1.\)

If the first and the nth term of a G.P. are a and b, respectively, and if P is the product of n terms, prove that P2 = (ab) n .

If a, b, c and d are in G.P. show that (a 2 + b 2 + c 2 ) (b 2 + c 2 + d 2 ) = (ab + bc + cd)2.
Find the value of n so that \(\frac{a^{n+1}+b^{n+1}}{a^n+b^n }\)n may be the geometric mean between a and b.
The sum of two numbers is 6 times their geometric mean, show that numbers are in the ratio (3+2√2) : (3-2√2).